The present invention relates to the measurement of the speed of sound. More specifically, the present invention relates to a method, and an arrangement for measuring the speed of sound based on the travel time of an acoustic signal through a predetermined distance.
FIG. 1 shows a prior-art arrangement 100 and method for measuring the speed of sound, as described in U.S. Pat. No. 4,926,395.
A control module 101 generates an output electrical pulse signal 102. The instance when the event starts, i.e. when the output electrical pulse signal 102 is generated, is denoted as t1. The output electrical pulse signal 102 is sent to a transmitting transducer 103.
The transmitting transducer 103 converts the output electrical pulse signal 102 into an acoustic pulse signal 104.
Next, the acoustic pulse signal 104 output by the transmitting transducer 103 travels through a medium 105, such as air or water, hits a reflector 106 and is reflected.
The reflected acoustic pulse signal 107 then travels back towards a receiving transducer 108 which receives the reflected acoustic pulse signal 107 and converts it into an electrical pulse signal which will be referred to in the following as reconstructed reflected electrical pulse signal 109.
In this known arrangement the front ends of the transmitting and receiving transducers lie in a plane parallel to the plane of the reflector 106, since the receiving transducer and the transmitting transducer are embodied by a single transducer.
Next, the reconstructed reflected electrical pulse signal 109 is sent to the control module 101.
Based on the instance when the reconstructed reflected electrical pulse signal 109 is received by the control module 101, the traveling time of the acoustic pulse signal, i.e. the time which was necessary for the output and reflected acoustic pulse signals to travel through the medium 105 is determined. The determination of the traveling time will be described below.
The speed of sound 110, s, determined and output by the control module 101 is given by                               s          =                                    2              ·              d                                      t              0                                      ,                            (        1        )            
where
d is the distance between the transmitting transducer 103 (or the receiving transducer 108) and the reflector 106, and
t0 is the traveling time which is the sum of the time needed for the output acoustic pulse signal 104 to travel through the distance between the transmitting transducer 103 and the reflector 106 and the time needed for the reflected acoustic pulse signal 107 to travel through the distance between the reflector 106 and the receiving transducer 108.
In the following, the determination of the traveling time t0 according to the state of the art will be described.
The output electrical pulse signal 102 generated by the control module 101 is typically a gated sinusoidal signal that is of a finite time duration, as shown in FIG. 2a. 
Due to the inherent characteristics of the transmitting transducer 103 and the receiving transducer 108, the transducers 103 and 104 will, in general, deteriorate the characteristics of the signals in the course of the respective signal conversion processes. This means for example that the waveform of the acoustic pulse signal 104 does not exactly correspond to the waveform of the output electrical pulse signal 102 from which it is generated by the transmitting transducer 103. Similarly, the waveform of the reconstructed reflected electrical pulse signal 109 does not exactly correspond to the waveform of the reflected acoustic pulse signal 107 from which the reconstructed reflected electrical pulse signal 109 is generated by the receiving transducer 108.
FIG. 2b shows an example of a reconstructed reflected electrical pulse signal 109 which is received by the control module 101 and originates from an input gated sinusoidal signal as the output electrical pulse signal 102 delivered to the transmitting transducer 103.
When the control module 101 receives a signal, it will decide whether the received signal is the reconstructed reflected electrical pulse signal 109 or just background noise.
For ease of discussion, the received signal is considered to be a digital signal.
When the control module 101 receives one digital sample of the received signal, it compares the amplitude of the current sample of the digital signal with two thresholds 301, 302, namely an upper threshold 301 and a lower threshold 302 (see FIG. 3).
In this context, amplitude is meant to be the voltage level of the digital signal at the current time instance.
If the absolute value of the amplitude of the current sample of the digital signal is larger than the absolute value of the upper or lower thresholds, the decision is that the reconstructed reflected electrical pulse signal 109 is detected, and this current time instance is then denoted by t2 (see FIG. 3).
Otherwise, the decision of the control module 101 is that the reconstructed reflected electrical pulse signal 109 is not detected, and the control module 101 continues to take the next digital sample and performs the comparison as described above until the reconstructed reflected electrical pulse signal 109 is detected.
The traveling time t0 is then estimated to be an estimated traveling time t0, which is given by
{circumflex over (t)}0=t2xe2x88x92t1,xe2x80x83xe2x80x83(2)
where
t1 is the time instance when the output electrical pulse signal 102 starts to be generated by the control module 101, and
t2 is the time instance when the reconstructed reflected electrical pulse signal 109 is detected by the control module 101.
This completes the description of how the traveling time t0 is estimated by the calculated time {circumflex over (t)}0.
However, the prior-art method described above particularly has two problems that cause the estimation of t0 by {circumflex over (t)}0 to be inaccurate.
Firstly, the conversion of the output electrical pulse signal 102 into its acoustic form (the acoustic pulse signal 104) by the transmitting transducer 103 is not instantaneous, mainly due to physical limitations of transducers. Indeed, there is a considerable time delay between the instance when the output electrical pulse signal 102 starts to be generated by the control module 101 (i.e., t1) and the instance when the acoustic pulse signal 104 starts to travel in the medium 105. If the delay is of a fixed value for different runs/scenarios of the speed-of-sound measurement, one could circumvent this problem by replacing t1 by t1 plus this fixed value. However, the delay is not constant for different runs/scenarios of the speed-of-sound measurement.
Secondly, the detection of the reconstructed reflected electrical pulse signal 109 is also not instantaneous. Indeed, the control module 101 can detect the arrival of the reconstructed reflected electrical pulse signal 109 only after a considerable time delay of about a few cycles of the reconstructed reflected electrical pulse signal 109, as shown in FIG. 3. If the delay is of a fixed value, for example one cycle for different runs/scenarios of the speed-of-sound measurement, one could circumvent this problem by replacing t2 by t2 minus this fixed value. However, also this delay is not constant for different runs/scenarios of the speed-of-sound measurement.
These problems become even worse when using low cost components, like a personal computer with a sound card as the control module 101, a commercial, rather low-cost loudspeaker as transmitting transducer 103, a plastic compact disc case as the reflector 106, and a commercial, rather low-cost microphone as the receiving transducer 108.
Thus, it is a first object of the present invention to provide an arrangement for measuring the speed of sound with improved accuracy particularly even when using low cost components, especially for educational purposes like for experimental speed-of-sound measurements in high schools.
To achieve the first object, according to a first aspect of the invention, an arrangement for measuring the speed of sound comprises an electrical pulse generating means for generating an electrical pulse signal which will be referred to in the following as output electrical pulse signal. The electrical pulse generating means is coupled, e.g. via a cable, to a transmitting transducer for converting the output electrical pulse signal into an acoustic pulse signal which will be referred to in the following as output acoustic pulse signal. The transmitting transducer may be a commercial, rather low-cost loudspeaker. Furthermore, a receiving transducer for converting an acoustic pulse signal into an electrical pulse signal is provided. The receiving transducer may be a commercial, rather low-cost microphone. Both transducers are coupled with a reflector in such a manner that the output acoustic pulse signal generated and output by the transmitting transducer is reflected by the reflector, thereby generating a reflected acoustic pulse signal which is received by the receiving transducer. According to this first aspect of the invention the receiving transducer is arranged, relative to the transmitting transducer, in such a manner that it receives both the output acoustic pulse signal and the reflected acoustic pulse signal and converts them to respective electrical pulse signals. The electrical pulse signal generated from the output acoustic pulse signal by the receiving transducer will be referred to in the following as reconstructed output electrical pulse signal, whereas the electrical pulse signal generated from the reflected acoustic pulse signal will be referred to in the following as reconstructed reflected electrical pulse signal. Furthermore, the arrangement according to this aspect of the invention comprises a speed determination means for determining the speed of sound using the reconstructed output electrical pulse signal and also the reconstructed reflected electrical pulse signal.
The electrical pulse generating means and/or the speed determination means may be implemented in a personal computer (PC). For example, both the electrical pulse generating means and the speed determination means may be implemented by a PC comprising a sound card.
Furthermore, the reflector may be a plastic element, in particular a compact disc case.
An advantage of the arrangement according to the invention can be seen in the fact that, even if very low-cost components are used, the accuracy of the speed-of-sound measurement is improved, since by determining the speed of sound based on the reconstructed output electrical pulse signal the uncertainty in the speed of sound calculation caused by the unknown time delay in the conversion process of transmitting transducer as described above in conjunction with the state of art arrangement is eliminated. Furthermore, this arrangement is very cheap and thus especially suitable for low-cost applications.
According to a further embodiment of the invention, the electrical pulse generating means is arranged in such a manner that it can generate an output electrical pulse signal with a waveform,
which begins with a dominant cycle with maximum amplitude, and
wherein the amplitude of the end portion of the output electrical pulse signal tapers off to either zero or a considerably smaller value as compared to the maximum amplitude of the output electrical pulse signal in its dominant cycle.
The output electrical pulse signal may further contain an initial portion whose amplitude is considerably smaller than the maximum amplitude of the output electrical pulse signal. For ease of discussion, the output electrical pulse signal is considered not to have such an initial portion.
With this embodiment of the invention, the robustness and the accuracy of the speed of sound measurement is further improved, since with such a waveform of the output electrical pulse signal the uncertainty in the speed of sound calculation caused by the unknown time delay in the detection process of the speed determination means as described above in conjunction with the state of art arrangement is eliminated or at least reduced.
According to a further embodiment of the invention, a wave guide is provided, which is arranged between the transmitting transducer and the reflector, and/or between the receiving transducer and the reflector.
Furthermore, the wave guide may be a hollow cylindrical tube, which is made by rolling a long piece of paper into a hollow cylinder.
With such a wave guide, the loss of signal energy is further reduced, thus providing better measurement results due to less reduction of the signal amplitude when traveling through the medium.
Furthermore, according to a preferred embodiment of the invention, the speed determination means is arranged in such a manner, that it determines the speed of sound using
a first instance, when the second peak of the dominant cycle of the reconstructed output electrical pulse signal is detected, and
a second instance, when the second peak of the dominant cycle of the reconstructed reflected electrical pulse signal is detected.
The second peak of the dominant cycle (which is the peak of the second half-cycle of the dominant cycle) of the reconstructed output electrical pulse signal is detected when its absolute value is larger than the absolute value of a first threshold, and the second peak of the dominant cycle of the reconstructed reflected electrical pulse signal is detected when its absolute value is larger than the absolute value of a second threshold. The first and second thresholds may have the same or different values. Preferably, the absolute value of the first threshold is larger than the absolute value of the second threshold, since in general the energy and, therefore, the amplitude of the reconstructed output electrical pulse signal is higher than that of the reconstructed reflected electrical pulse signal.
According to the invention it is advantageous to choose the second half-cycle instead of the first half-cycle, since it was observed that in some scenarios, the peak of the first half-cycle of the dominant cycle of the reconstructed reflected electrical pulse signal is not significant enough, while in other scenarios it is significant enough, i.e., the absolute value of which is, on some occasions, smaller than the absolute value of the second threshold, but on other occasions larger. Therefore, detecting the peak of the first half-cycle of the dominant cycle would in many cases affect the accuracy of estimating the traveling time t0, since in some occasions the time at which a peak is detected would correctly correspond to the peak of the first half-cycle of the dominant cycle, but it would, in other occasions, incorrectly correspond to the peak of the first half-cycle of a cycle following the dominant cycle, because the peak of the first half-cycle of the dominant cycle is not detected. On the other hand, the peak of the second half-cycle of the dominant cycle of the reconstructed reflected electrical pulse signal is consistently significant enough.
Further, it is a second object of the present invention to provide a method for measuring the speed of sound with improved accuracy particularly even when using low cost components.
To achieve the second object, an output electrical pulse signal is generated in a first step of the method for measuring the speed of sound according to a second aspect the invention. Next, the output electrical pulse signal is converted into an output acoustic pulse signal. After having been reflected by a reflector, the thus generated reflected acoustic pulse signal is received and converted into a reconstructed reflected electrical pulse signal. As a last step, the speed of sound is determined using the reconstructed reflected electrical pulse signal.
Furthermore, according to a preferred embodiment of the invention, an output electrical pulse signal is generated in a first step of the method for measuring the speed of sound according to a second aspect the invention. Next, the output electrical pulse signal is converted into an output acoustic pulse signal and into a reconstructed output electrical pulse signal. After having been reflected by a reflector, the thus generated reflected acoustic pulse signal is received and converted into a reconstructed reflected electrical pulse signal. As a last step, the speed of sound is determined using the reconstructed reflected electrical pulse signal and the reconstructed output electrical pulse signal.
The embodiments described above with reference to the arrangement do apply as well to the method according to the present invention.